Chapter 10
Fluids
Units of Chapter 10
•Phases of Matter
•Density
•Pressure in Fluids
•Atmospheric Pressure and Gauge Pressure
•Pascal’s Principle
•Measurement of Pressure; Gauges and the
Barometer
•Buoyancy and Archimedes’ Principle
Units of Chapter 10
•Fluids in Motion; Flow Rate and the Equation of
Continuity
•Bernoulli’s Equation
•Applications of Bernoulli’s Principle: from
Torricelli to Airplanes, Baseballs, and TIA
•Viscosity
•Flow in Tubes: Poiseuille’s Equation, Blood Flow
•Surface Tension and Capillarity
•Pumps, and the Heart
10-1 Phases of Matter
The three common phases of matter are solid,
liquid, and gas.
A solid has a definite shape and size.
A liquid has a fixed volume but can be any
shape.
A gas can be any shape and also can be easily
compressed.
Liquids and gases both flow, and are called
fluids.
10-2 Density and Specific Gravity
The density ρ of an object is its mass per unit
volume:
(10-1)
The SI unit for density is kg/m3. Density is also
sometimes given in g/cm3; to convert g/cm3 to
kg/m3, multiply by 1000.
Water at 4°C has a density of 1 g/cm3 = 1000 kg/m3.
10-3 Pressure in Fluids
Pressure is defined as the force per unit area.
Pressure is a scalar; the units of pressure in the
SI system are pascals:
1 Pa = 1 N/m2
Pressure is the same in every
direction in a fluid at a given
depth; if it were not, the fluid
would flow.
10-3 Pressure in Fluids
Also for a fluid at rest, there is no
component of force parallel to any
solid surface – once again, if there
were the fluid would flow.
10-3 Pressure in Fluids
The pressure at a depth h below the surface of
the liquid is due to the weight of the liquid above
it. We can quickly calculate:
(10-3)
This relation is valid
for any liquid whose
density does not
change with depth.
10-4 Atmospheric Pressure and Gauge
Pressure
At sea level the atmospheric pressure is about
; this is called one
atmosphere (atm).
Another unit of pressure is the bar:
Standard atmospheric pressure is just over 1 bar.
This pressure does not crush us, as our cells
maintain an internal pressure that balances it.
10-4 Atmospheric Pressure and Gauge
Pressure
Most pressure gauges measure the pressure
above the atmospheric pressure – this is called
the gauge pressure.
The absolute pressure is the sum of the
atmospheric pressure and the gauge pressure.
10-6 Measurement of Pressure; Gauges and
the Barometer
There are a number of different types of
pressure gauges. This one is an opentube manometer. The pressure in the
open end is atmospheric pressure; the
pressure being measured will cause
the fluid to rise until
the pressures on both
sides at the same
height are equal.
10-6 Measurement of Pressure; Gauges and
the Barometer
Here are two more devices for
measuring pressure: the
aneroid gauge and the tire
pressure gauge.
10-6 Measurement of Pressure; Gauges and
the Barometer
This is a mercury barometer,
developed by Torricelli to
measure atmospheric pressure.
The height of the column of
mercury is such that the pressure
in the tube at the surface level is 1
atm.
Therefore, pressure is often
quoted in millimeters (or inches)
of mercury.
10-6 Measurement of Pressure; Gauges and
the Barometer
Any liquid can serve in a
Torricelli-style barometer,
but the most dense ones
are the most convenient.
This barometer uses water.
10-7 Buoyancy and Archimedes’ Principle
This is an object submerged in a fluid. There is a
net force on the object because the pressures at
the top and bottom of it are different.
The buoyant force is
found to be the upward
force on the same volume
of water:
10-7 Buoyancy and Archimedes’ Principle
The net force on the object is then the difference
between the buoyant force and the gravitational
force.
10-7 Buoyancy and Archimedes’ Principle
If the object’s density is less than that of water,
there will be an upward net force on it, and it will
rise until it is partially out of the water.
10-7 Buoyancy and Archimedes’ Principle
For a floating object, the fraction that is
submerged is given by the ratio of the object’s
density to that of the fluid.
10-7 Buoyancy and Archimedes’ Principle
This principle also works in
the air; this is why hot-air and
helium balloons rise.
Summary of Chapter 10
• Phases of matter: solid, liquid, gas.
• Liquids and gases are called fluids.
• Density is mass per unit volume.
• Specific gravity is the ratio of the density of the
material to that of water.
• Pressure is force per unit area.
• Pressure at a depth h is ρgh.
• External pressure applied to a confined fluid is
transmitted throughout the fluid.
Summary of Chapter 10
• Atmospheric pressure is measured with a
barometer.
• Gauge pressure is the total pressure minus the
atmospheric pressure.
• An object submerged partly or wholly in a fluid
is buoyed up by a force equal to the weight of
the fluid it displaces.
• Fluid flow can be laminar or turbulent.
• The product of the cross-sectional area and the
speed is constant for horizontal flow.